Actually, when I looked up the route, I found it is only 1500 miles or so one way (via Salt Lake City).

So you'd only have a 3000 mile trip. Still a long way to go in 10 days, but it is much more manageable. Assuming you are planning to spend a couple days in LA, you'll still probably be looking at 400-500 mile days, which is long, but feasable.