A fabulous number

Let \(n\) be an integer greater than \(1\). The positive divisors of \(n\) are \({ d }_{ 1 },{ d }_{ 2 },\ldots,{ d }_{ k }\), in which \(1={ d }_{ 1 }<{ d }_{ 2 }<\ldots<{ d }_{ k }=n\). If \(n\) satisfies \(n={ d }_{ 2 }^{ 2 }+{ d }_{ 3 }^{ 3 }\), what is the sum of all the possible values of \(n\)?


This problem appeared at the Mexican MO.
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