The 11,000# is a MAXIMUM for the truck based on a base model truck, no passenger (only a 150# driver), no cargo, no hitch. So for every pound you add to the base truck, you reduce the towing rating by the same amount. To know what you can truly haul/pull within ratings, you need to load up the truck with family, cargo, hitch, full fuel, etc and get weights on the front and rear axles as well as total weight. Now the owners manual will have a GCWR (gross combined weight rating) for your cab/engine and axle combination. On the drivers door you will have a sticker giving the front and rear axle GAWR. There will also be a GWVR (gross vehicle weight rating).
Now:
GVWR - loaded truck = Max loaded trailer hitch weight.
GCWR - loaded truck = Max loaded total trailer weight.
You can pretty much forget the brochure dry weight and hitch weight. A bumper pull travel trailer will have a loaded hitch weight of 10 to 15% of the trailer GVWR.
Any item in the brochure listed as option needs to be added to the dry weight. Things like awnings, microwave, A/C, batteries are not include, but are options. Now you add some water, two 30# propane tanks, food, clothing, camping chairs, fishing tackle, kids bikes and suddenly your trailer is 1000# plus over the dry weight.
Your weight sounds light for a 37' trailer. Next, I would not try pulling a 37' trailer with a 1/2 ton truck. You will truly have the tail wagging the dog.
And Yes, you can always pull more than the truck is rated to pull, but should you. You see people doing it every day. Are they having fun...probably not. It is a lot more work to pull with too little truck than an adequately sized truck. We have been the route of too small of a vehicle for the trailer we had. Not fun and longer trips were tiring.
We have a 2012 F350 Dually and a 36' Cameo trailer and they do well together. The truck is well within ratings fro this trailer.
Ken