Wait... does this even exist?

Let \(n\) be a positive integer such that

\(a^{3}+b^{3}=n\)

\(c^{3}+d^{3}=n\)

Where \(a\), \(b\), \(c\) and \(d\) are distinct, positive integers. What is the smallest possible value of \(n\)?

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