This yields a differential equation in V[t].

Input := 


sol = DSolve[V'[t] == - k (36 Pi)^(1/3)  V[t]^(2/3), V[t],t]

Output =


                      1/3

           -(k (36 Pi)    t)        3

{{V[t] -> (----------------- + C[1]) }, {V[t] -> 0}}

                   3