Let $P_1$ be the plane $3 x-y-7 z=11$ and $P_2$ be the plane passing through the points $(2,-1,0),(2,0,-1)$, and $(5,1,1)$. If the foot of the perpendicular drawn from the point $(7,4,-1)$ on the line of intersection of the planes $P_1$ and $P_2$ is $(\alpha, \beta, \gamma)$, then $\alpha+\beta+\gamma$ is equal to $\_\_\_\_$ .