There is no conflict. It is more misunderstanding than anything. We do not believe that we can get to heaven only by doing things or earning our way there. It is through God's grace and the Savior's atonement that we can be sanctified and saved. 
 
Let me provide a simple analogy (that is purely hypothetical). Let's say you are living in the midwest of North America in the 1700s. Your end goal is to get to Hawaii. There is only one way to get there - by getting on a ship that leaves from Los Angeles and sails to Hawaii. There is one and only one ship that goes there - so you have to get on that ship. But to get to that ship you have to make the long journey from the midwest to Los Angeles (assuming Los Angeles existed in the 1700s) by yourself. As long as we make it to Los Angeles then we will have a free ride on the ship to Hawaii - our end destination. 
 
We believe that our journey from the midwest to Los Angeles is what we have to do ourselves to make it to Hawaii. The ride on the ship from Los Angeles to Hawaii is the part that God does for us. We have no ability to go from Los Angeles to Hawaii on our own. We are totally dependent on that ship. In this analogy us keeping the commandments and doing all we can do is what we do to get from the midwest to Los Angeles. Once we get to Los Angeles - the ship ride is what God provides free to us (Grace). Both parts are necessary. The ship does not sail from the midwest. We cannot on our own get from Los Angeles to Hawaii. 
 
I know this analogy will have flaws - but it's just a simple illustration showing that we have to do our part - so that God can do his. We absolutely believe in Grace - 'we are saved after all we can do'. We get a free ship ride - after we have put forth the effort to put us in a position to receive it.

Here is a link to a good explanation of it being more misunderstanding that difference: 
 
http://en.fairmormon.org/Mormonism_and_Christianity/Grace_and_works/Salvation_by_faith_alone

Latter-day Saints also believe that we are saved by the grace of Jesus Christ, whom ever told you differently lied to you, but we also believe that to be said by grace one must have faith in the Lord Jesus Christ.  
 
Without faith in Jesus Christ we cannot receive his grace, just as we are told in the scriptures, "For by grace are ye saved through faith; and that not of yourselves: it is the gift of God" (Ephesians 2:8) 
 
So one must have faith to receive Christ's grace, anyone who teaches otherwise is a false teacher, and seeks to deceive and keep you from Christ.  
 
 
Now let's look at what scripture have to say about faith, "Even so faith, if it hath not works, is dead, being alone." (James 2:17)  
 
So if state you have faith but you have no actions to support that statement your faith is dead. To say one has faith but not take any actions to show that faith to the Lord, is to be as a Pharisee and say one thing and do another. Christ doesn't look kindly on hypocrites, without works you have no faith, and without faith you cannot receive the grace of the Lord.  
 
I hope that this clarifies the misunderstanding you have, understand that if you only expect to be saved by grace alone, and that you will not have to do anything to receive that grace, you have been lied to. Stop such deception and live according to the Word of God instead of the traditions of man.  
 
Feel free to visi www.mormon.org to learn more restored truths like this one!