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 $a/b$, where $a$ and $b$ are positive integers and $\gcd(a, b) = 1$. Find $a+b$. 

Let's think step by step and output the final answer within \boxed{}.
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