Triangle-Ception II

Geometry Level 5

Quadrilateral ABCDABCD is an isosceles trapezoid with AB=6,BC=6,CD=12,AD=6AB=6,BC=6,CD=12,AD=6.

Points XX and YY are chosen on sides ADAD and DCDC respectively, such that DX=qDX=q and DY=pDY=p.

If the area of triangle XYBXYB is 11311\sqrt{3}, the minimum value of pqp-q can be expressed in the form mnm\sqrt{n}, where nn is not divisible by the square of any prime. Find m+nm+n.

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