Basically the signals coming from the D* dish and and a V* dish are the same frequencies.
(the reason why Cable Internet and TV can co-exist on the same cable is that they are transmitted at different frequencies).
So, no you can't really have both going through one cable.
But I can envision a not too-complicated setup using a standard DirecTV multiswitch and a 22kHz tone inserter where you could manually switch between the two satellite providers coming through one cable (assuming you only want/need the 101 satellite for DirecTV).
You'd turn on the 22kHz tone to watch one provider, and turn it off to watch the other... You'd have to run two lines from the Voom dish and two lines from the 101 LNB of a DirecTV dish to the multiswitch, and then one output into your house.
But if you want/need the 110 or 119 satellites for DirecTV, or don't want to deal with this complicated setup - it just might be easier to bite the bullet and run that second line.