It slants just fine

Geometry Level 4

Square ABCD has sides of length 1. Points E and F are on \(\overline{BC}\) and \(\overline{CD}\) , respectively, so that \(\triangle AEF\) is equilateral. A square with vertex B has sides that are parallel to those of ABCD and a vertex on \(\overline{AE}\) . The length of a side of this smaller square is \(\dfrac{a-\sqrt{b}}{c}\) , where \(a,b\) , and \(c\) are positive integers and \(b\) is not divisible by the square of any prime. Find \(a+b+c\).

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