A triangle has an area of $30$, one side of length $10$, and the median to that side has a length of $9$. Let $\theta$ be the acute angle formed by that side and the median. The original answer for $\sin{\theta}$ is in the form \frac{k}{m}. Please provide the value of k + m.

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