Talk:2013 AMC 12B Problems/Problem 25

Given a trapezoid with bases $AB$ and $CD$ , there exists a point $E$ on $CD$ such that drawing the segments $AE$ and $BE$ partitions the trapezoid into $3$ similar isosceles triangles, each with long side twice the short side. What is the sum of all possible values of $\frac{CD}{AB}$ ?The answer is in the form �rac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.