Let $A$ be the area of the region in the first quadrant bounded by the line $y=\frac{1}{2} x$, the $x$-axis, and the ellipse $\frac{1}{9} x^{2}+y^{2}=1$. Find the positive number $m$ such that $A$ is equal to the area of the region in the first quadrant bounded by the line $y=m x$, the $y$-axis, and the ellipse $\frac{1}{9} x^{2}+y^{2}=1$.The answer is in the form \frac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.

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