Dump trucks are equipped with a hydraulic piston that raises and
lowers the bed.
The beds of dump trucks are controlled by a hydraulic pump.
There's a good video about the process on YouTube.
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If the dump is run by a pto you can tow it in gear (you said
manual trans) with the pto engaged and you should be able to raise
the dump box. There is a lift fuel pump in each tank and a high
pressure pump on the frame rail below the drivers door area.