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 \(m+n\).
(第十八届AIME2 2000 第11题)