Let the equation of plane passing through the line of intersection of the planes x+2 y+a z=2 and x-y+z=3 be 5 x-11 y+b z=6 a-1. For c ∈ Z, if the…

Let the equation of plane passing through the line of intersection of the planes $\displaystyle x+2 y+a z=2$ and $\displaystyle x-y+z=3$ be $\displaystyle 5 x-11 y+b z=6 a-1$. For $\displaystyle c \in \mathbb{Z}$, if the distance of this plane from the point $\displaystyle (a,-c, c)$ is $\displaystyle \frac{2}{\sqrt{a}}$, then $\displaystyle \frac{a+b}{c}$ is equal to