Find $\det A$ and $Tr A$ if $\det(A+\sqrt[n]{3}I_n)=0$

$ A \in M_{n}(\mathbb{C})$ and I have to find $ \det A$ and $ Tr A$ if $ \det(A+\sqrt[n]{3}I_n)=0$ . I observed that $ \sqrt[n]{3}$ is an eigenvalue of $ A$ ,but I don’t know how to continue.