I think that this one needs integrating factors.
What I would do is divide everything by mv, and then take the (vx^x)/m term to the other side. This will give you the standard form of a non-separable first order ode (google this if you are unsure of the method). Your integrating factor is then e^(-int (x^x)/m) - but this is very hard to integrate. You could then rearrange and solve for v(x).