Tetrahedron \(ABCD\) has \(AB=5\), \(AC=3\), \(BC=4\), \(BD=4\), \(AD=3\), and \(CD=\tfrac{12}{5}\sqrt{2}\). Find the volume of the tetrahedron. The original answer is in \(\frac{k}{m}\) format, please give the value of \(k + m\).

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