$p(x)=x^7-x^4$ is surjective, so for each $y$, there is at least one $x$ satisfying the equation.

Set $x=dy$ $y^7(d^7+1)=y^4(d^4+1)$ $y=(\dfrac{d^4+1}{d^7+1})^{\dfrac{1}{3}}$ $x=d(\dfrac{d^4+1}{d^7+1})^{\dfrac{1}{3}}$