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)