Let \triangle A B C be a triangle with circumcenter O and orthocenter H. Let D be a point on the circumcircle of A B C such that A D \perp B C. Suppose that A B=6, D B=2, and the ratio \frac{\operatorname{area}(\triangle A B C)}{\operatorname{area}(\triangle H B C)}=5. Then, if O A is the length of the circumradius, then O A^{2} can be written in the form \frac{m}{n}, where m, n are relatively prime nonnegative integers. Compute m+n.
Note: The circumradius is the radius of the circumcircle.