Clutches generally go under heavy load... at 6000rpm in the right gear, there isnt actually much load on the clutch.
Go out on the highway, and stomp on it in a taller gear, and that will generally apply alot more load causing the clutch to slip.
In your case the clutch does sound fried tho, but its a very quick death. Are you sure you didnt try to do a line locky and smoke the clutch instead of the tires