2000 AIME II Problem 11

The coordinates of the vertices of isosceles trapezoid ABCD are all integers, with A=(20,100) and D=(21,107). The trapezoid has no horizontal or vertical sides, and \overline{AB} and \overline{CD} are the only parallel sides. The sum of the absolute values of all possible slopes for \overline{AB} is m/n, where m and n are relatively prime positive integers. Find m+n.

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.