Infinite Nested Radicals

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

What is the value of $n$ ?

This problem is inspired by Adam Pet's Infinite factorials problem