The $$\(n\)$$th term of an arithmetic series is $$\(u_{n}\)$$ where $$\(u_{n}> 0\)$$ for all $$\(n\)$$ The sum to $$\(n\)$$ terms of the series is $$\(S_{n}\)$$ Given that $$\(u_{4}=6\)$$ and that $$\(S_{11}=\left(u_{6}\right)^{2}+18\)$$ find the value of $$\(u_{20}\)$$

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