Trapezoid A B C D has \overline{A B} \| \overline{C D}, B C=C D=43, and \overline{A D} \perp \overline{B D}. Let O be the intersection of the diagonals \overline{A C} and \overline{B D}, and let P be the midpoint of \overline{B D}. Given that O P=11, the length A D can be written in the form m \sqrt{n}, where m and n are positive integers and n is not divisible by the square of any prime. What is m+n ?

**Answer Choices**

A. 65

B. 132

C. 157

D. 194

E. 215