A regular cab F550 diesel, with a 1,000 lb body weight - (dump cart, but it is prolly more than 1K) - can bumper pull a max 16,000 pounds.
The GVWR is on the door pillar tag. It is the max loaded weight of truck and trailer.
Be sure you have the right load rating tires for both truck and trailer, the DOT will focus on that.
If you have short sides on the dump, say 18" and under, a gooseneck is the way to go.
You can haul a 24,500 lb gooseneck, and they are far better to manuver. Not really that much more money to buy either..I have a 2000 PDS 4x4 F550, and I want a 25K dual tandem deckover gooseneck dump. The sides come off, making it a deckover, and it's a full 8' wide inside the sideboards. The trailer will tare in around 10,000lbs, so I'd have a 15K payload...look into them. Search google for "craig'slist", use the apostrophe...a search box will come up and you can search all of craigslist for a trailer. The 25K D-T deckover gooseneck dump can be found in the south for $6,000-$10,000.