Even if the weight is under the 7k max rating, it's not as much as a "Can it do it?" as a "Should you do it?"
If weight is lower than 6500, it could do it but that thing is pretty big and has A LOT of cross section to catch wind. That's a pretty long trip through some windy areas with something like that. Like someone said, if you're not in any hurry it would be better but doing anything close to the max isn't necessarily a good idea even though it technically can do it.
Also the v6 has a built in trans cooler iirc. Forgot if its separate or built into the radiator.
2016 Red Rock
LT CC SB v6 4x4
Eibach Shocks all around w/GM rear blocks, Dee Zee bed mat, TruXedo tonneau, Bull rings, Zevo LEDs, Westin steps, Fog Lights w/JDMAstar LED, Rear LED pods, Lumen G7s LED Headlights, Factory Remote Start, Dash Cam w/Invisicord, Husky Liners, Canyon console lid, Black badges and grill, Trifecta
My build thread
Front bumper removal How-To
Rear Shock/lift Blocks How-To