Find all the solutions of $\displaystyle x^3+3x-8\equiv 0mod(33)$

I can only see

$\displaystyle x^3+3x-8\equiv 0 mod(3)$ and $\displaystyle x^3+3x-8 \equiv 0 mod(11)$

however i cannot seem to condense these further and mod 11 by inspection does seem right