It slants just fine

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 $a+b+c$ .