Uniquely defined

\[\LARGE {{\color{blue}n}{\color{red}!} = {\color{blue}n}^{\color{red}2} + {\color{blue}n}^{\color{red}{\frac{3}{2}}} }\]

Find the sum of value(s) of positive integer \(n\).

This problem is a part of the set Easy Factorials.
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