In triangle \(ABC\), the median from vertex \(A\) is perpendicular to the median from vertex \(B\). If the lengths of sides \(AC\) and \(BC\) are \(6\) and \(7\) respectively, find the length of side \(AB\). The original answer is in the form \(\sqrt{k}\). Please find the value of \(k\).

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