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Number Theory Level pending

This problem is the new version of my previously posted question, which received many reports because of lack of details.

If a, b, c, and d are positive integers such that

\(a^{3} = b^{2}\)

\(c^{3} = d^{2}\)

\(c - a = 5\)

Find the value of \(c + a\).

Hint:It's not necessary to solve for b and d.


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