Probably can pull it, probably should not.
I have a 2004 F350 with the powerstroke diesel. When we first started the mulching business, I pulled our Bobcat T320 with mulcher on a 21' gooseneck trailer. Sometimes with a bucket or brush cutter as well. It was hard on the truck and I tried to be real easy.
One day I was coming back from a job with nothing but the bobcat and mulcher on the trailer. Stopped for fuel at a place that just happened to have a truck scale and I couldn't resist. Turns out, I was just over 27,000 lbs. I was tagged for 26,000 lbs which is well over recommended. If I were to tag the truck for enough to pull the equipment you would have to have a CDL to drive it. I do, but my wife doesn't.
Look around and you can find a used single axle tractor for pretty reasonable (less than a F250 in many cases) or a tandem axle dump truck. The dump truck with a 10 ton tag along trailer makes a good combo and will expand your possibilities. You will have to get a CDL.