Let \( L=\lim _{n \rightarrow \infty} n\left(\sqrt[3]{n^{3}+3 n^{2}...

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Let \( L=\lim _{n \rightarrow \infty} n\left(\sqrt[3]{n^{3}+3 n^{2}+2 n+1}+\sqrt{n^{2}-2 n+3}-2 n\right) \). If \( L \) can be expressed in the
P form of \( \frac{p}{q}(p, q \in N) \) in the lowest form then find the value of \( (p+q) \).

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