Solving $aX^3 + bY^3 + cZ^3 - dXYZ = 0$ over $\mathbb{F}_q$

Question

I am looking for a way to solve the equation mentioned in the title with $Z\neq 0$ over the finite field $\mathbb{F}_q$ without going through all $q^3$ possibilities. I was thinking: maybe we can reduce it to searching through only $q^2$ elements using which elements are cubes in $\mathbb{F}_q$. Any help would be appreciated!