2011 AIME I Problem 3

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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.