The fraction \(\frac{2(\sqrt{2} + \sqrt{6})}{3\sqrt{2 + \sqrt{3}}}\) is equal to what value? The answer is in the form \(\frac{k}{m}\), where \(\frac{k}{m}\) is a simplified fraction. Please calculate the value of \(k + m\).

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