Let L be the line with slope \frac{5}{12} that contains the point A=(24,-1), and let M be the line perpendicular to line L that contains the point B=(5,6). The original coordinate axes are erased, and line L is made the x-axis and line M the y-axis. In the new coordinate system, point A is on the positive x-axis, and point B is on the positive y-axis. The point P with coordinates (-14,27) in the original system has coordinates (\alpha, \beta) in the new coordinate system. Find \alpha+\beta.