\[ \sqrt { 10n\times \sqrt { n\sqrt { n\sqrt { n\ldots } } } \times \sqrt { (n-1)\sqrt { (n-1)\sqrt { (n-1)\ldots } } \times \ldots\times \sqrt { 3\sqrt { 3\sqrt { 3\ldots} } } } } =60n\]

What is the value of \(n\)?

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