Let \triangle A B C be an acute triangle with circumcircle \omega, and let H be the intersection of the altitudes of \triangle A B C. Suppose the tangent to the circumcircle of \triangle H B C at H intersects \omega at points X and Y with H A=3, H X=2, and H Y=6. The area of \triangle A B C can be written as m \sqrt{n}, where m and n are positive integers, and n is not divisible by the square of any prime. Find m+n.