Plane Equation Distance and Integer Value

Let the equation of plane passing through the line of intersection of the planes x+2y+az=2 and x−y+z=3 be 5x −11y+bz=6a−1. For c∈Z, if the distance of this plane from the point (a,−c,c) is ‌

2

√a

, then ‌

a+b

c

is equal to