Let \( P_{1} \) be the plane \( 3x-y-7z=11 \) 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 _______.
