Hello, James here. What engine is in your F350?
If you have a hand vacuum pump, I've had some luck applying vacuum to the top of the dipstick tube at least moving the broken stick a little until you can get some needle nose pliers onto the broken piece. If pliers won't grab, try to carefully tag into the outside perimeter of the broken stick with a small mechanics pick. If none of the above is successful or you have already tried all of this, here is the procedure to remove the dipstick tube. You likely won't have to take it all the way out. If you can unbolt it and slide the tube out enough, you should be able to grab the bottom of the stick with needle nose pliers and force it out from the bottom.
Removal and Installation
NOTICE: The coolant hose clamps used on this engine are constant tension worm gear clamps. Standard worm gear clamps cannot be used. Failure to use the correct coolant hose clamps may result in hose joint failure.