Show that the eigenvalues of $A+B$ is the sum of eigenvalues of $A$ and $B$.

Question

Let $A, B\in M_n(\mathbb{C})$ s.t. $AB=BA$. Show that the eigenvalues of $A+B$ is the sum of eigenvalues of $A$ and $B$.

First I tried to find a counterexample and I found out this property without proof.