Let $\vec a,\vec b,\vec c$ be three non-zero vectors such that $\vec b$ and $\vec c$ are non-collinear. If $\vec a+5\vec b$ is collinear with $\vec c$, $\ \vec b+6\vec c$ is collinear with $\vec a$ and $\vec a+\alpha\vec b+\beta\vec c=\vec 0$, then $\alpha+\beta$ is equal to: