Uniquely defined

Number Theory Level 2

n!=n2+n32\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 nn.

This problem is a part of the set Easy Factorials.
Brilliant Member by Brilliant Member
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