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 $\vec c$, and $\ \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: