Uniquely defined

n!=n2+n32\LARGE {{\color{#3D99F6}n}{\color{#D61F06}!} = {\color{#3D99F6}n}^{\color{#D61F06}2} + {\color{#3D99F6}n}^{\color{#D61F06}{\frac{3}{2}}} }

Find the sum of value(s) of positive integer nn.

This problem is a part of the set Easy Factorials.
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