Let \omega_1 be a circle of radius 6, and let \omega_2 be a circle of radius $5$$ that passes through the center O of \omega_1. Let A and B be the points of intersection of the two circles, and let P be a point on major arc AB of \omega_2. Let M and N be the second intersections of PA and PB with \omega_1, respectively. Let S be the midpoint of MN. As P ranges over major arc AB of \omega_2, the minimum length of segment SA is \frac{a}{b}, where a and b are positive integers and \gcd(a, b) = 1. Find a + b.