Given a right triangle $ABC$ with legs $BC=3$ and $AC=4$, find the length of the shorter angle trisector from $C$ to the hypotenuse. Provide your answer in the form \(\frac{k\sqrt{m}-n}{p}\), and then find the value of k + m + n + p.

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