I would proceed with caution and get yourself up to expert status on all of the weight parameters: Gross combined, axle, tow. You will be pushing the limits with that rig. I'm sure the truck can pull the trailer, but it's a bad day coming DOWN the mountain when you discover you can't stop the rig.
With 6 average adults in seats and towing my rig for a full summer jaunt, I'm 700# over GCWR with my Suburban towing a 19' Rockwood Roo (tanks empty). I was surprised I was over when I hit the scales. (Where did that weight come from...we packed light?!) I only proceeded because all axle weights, tongue weight and other parameters were still in limits. Needless to say, I drive VERY conservatively on mountain roads.