7555 before your wife loads it up! Then it will be like 9,000 pounds.
Your maximum tow rating is 7,800 pounds. The most your truck and trailer can weigh together is 14,000 pounds.
If you were to tow a trailer that weighs 7,555 pounds with your rig, the most weight you could have in the cab of the truck would be about 400 pounds.
Do a search for Dave's Denalis and towing.
@Geotrash He drags a 7,200 pound travel trailer (loaded weight) all over the country with his Yukon XL Denalis. I think the trailer actually weighs somewhere around 6,400 pounds empty.
I think it best to keep the length of the trailer at no more than 32 feet or so. A high sail area is going to blow you all over the road with that 1500 chassis. A Pro-Pride hitch will help with that though. Unless of course you are making short trips on relatively flat land, then pull what you feel comfortable with. I know of guys that haul 65 foot speedboats to and from the boat ramp with their Denalis and Escalades, the short ones!