Let a, b and c be three non-zero vectors such that b and c are non-collinear. If a +5 b is collinear with c, b +6 c is collinear with a and a +α b +β…

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