Welcome,
Your dump bed truck is almost certainly a C&C - cab and chassis - which uses a different frame than the regular pickups. The profile of it is essentially flat once it kicks up behind the cab, the rails are ladder-straight, and 34" apart. They are 4" longer than regular pickup trucks as far as wheelbase goes. This is a universal arrangement that allows for any number of work-style beds to be bolted up. Dump bed, flat bed, utility box, wrecker unit, etc. Another thing the C&C trucks almost always get is a narrower rear axle - by about 8". If your inside rear tires are directly in line with your fronts, you have the narrow rear axle.
So with all that said, a normal dually pickup bed will not bolt right up. You could make mounts for it, but there will be a larger gap between the cab and front of the bed, and the rear wheels will sit deep inside the fenders.
There's a number of ways to go about this and plenty of people have done it, but as you can see there's a lot of details to cover.
Beyond all that.. post pics! We love pics. Is it a real 3500HD (straight axle front end, 19.5" 10 lug wheels) or an 8 lug 3500 1 ton?
Richard