Given $\det \begin{pmatrix} x & y & z \\ 1 & 2 & 3 \\ 4 & 5 & 6 \end{pmatrix} = 10$, what is the determinant of $\begin{pmatrix} x+1 & y+2 & z+3 \\ 1 & 2 & 3 \\ 4 & 5 & 6 \end{pmatrix}$?