If the area of \(\triangle ABC\) is \(64\) square units and the geometric mean (mean proportional) between sides \(AB\) and \(AC\) is \(12\) inches, find the value of \(\sin A\). The answer should be in the format \(\frac{k}{m}\), where \(\frac{k}{m}\) is a simplified fraction. Please provide the value of \(k + m\).

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