On a map with a scale of \( 400 \) miles to an inch and a half, a certain estate is represented by a rhombus with a \( 60^{\circ} \) angle. The diagonal opposite the \( 60^{\circ} \) angle is \( \frac{3}{16} \) inches. Calculate the area of the estate in square miles. The original answer is in the form of \( k\sqrt{m} \). Please provide the value of \( k + m \).

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