Just for reference I am doing something similar. I currently have a Ram 2500 that tows a Carriage 30ft fiver. The fifth wheel has a dry weight of close to 11,400lbs and tops out just over 14,000 loaded. I don't have the exact numbers, but have never had an issue.
My truck is a little older, it is an '03 Cummins with the 5.9 not the 6.7. I also live in Newfoundland, so I have numerous hills when I tow. I have so far, only found one hill to really slow me down, on the west coast of the island. I don't have any mountains like Colorado has but haven't had an issue in about five years of towing.
