If the equation of the plane passing through the line of intersection of the planes \(2 x-y+z=3,\) \(4 x-3 y+5 z+9=0\) a…

If the equation of the plane passing through the line of intersection of the planes \(2 x-y+z=3,\) \(4 x-3 y+5 z+9=0\) and parallel to the line \(\frac{x+1}{-2}=\frac{y+3}{4}=\frac{z-2}{5}\) is \(a x+b y+\) \(c z+6=0\). then \(a+b+c\) is equal to

[JEE Main 2023, 6 Apr (Shift 1)]