To figure out how much weight you can tow, you need to find the most limiting factor of the vehicle. Ignore the 11K lbs tow rating. That is pie in the sky.
Look for the payload capacity of your truck. There is a tire inflation sticker inside the driver door jamb that says something like "Weight of cargo not to exceed ____ pounds". That is what the vehicle can carry.
Starting with that number, subtract the weight of passengers, anything else to be carried in the bed, and 100lbs for the weight distrib hitch.
What is left over is how much trailer tongue weight the vehicle can carry.
For stability, a TT needs 12 to 15% of it's loaded up to camp weight on the tongue. Now take the vehicle's left over carry capacity and divide that by .15
What you have, is the maximum weight your vehicle should tow based on it's payload capacity.
As an example:
My 3/4 Suburban has a payload of 2000#. Passengers can be up to 800#. WDH 100#.
2000 - 800 - 100 = 1100.
1100 / .15 = 7333
My TT loads up at 7200# with 1100# hitch weight ready to camp. I am just within(barely) payload capacity.
The tow rating on my truck is 10,500#. So you can see how payload is the limiting factor for my vehicle.