In \(\triangle ABC\), points \(D\) and \(E\) lie on \(BC\) and \(AC\), respectively. If \(AD\) and \(BE\) intersect at \(T\) so that \(\frac{AT}{DT}=3\) and \(\frac{BT}{ET}=4\), find the value of \(\frac{CD}{BD}\). 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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