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Calculus Level 5

If \( \displaystyle \lim_{n \to \infty} \left(\frac{{5n \choose 2n}}{{3n \choose 2n}} \right)^{\frac{1}{n}}\) can be expressed as \(\dfrac{p}{q}\), for coprimes \(p\) and \(q\), what is the value of \(p+q?\)

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