Try a problem by Titu Andreescu

Algebra Level 5

Find the number of triple/triples of rational numbers \((a, b, c)\) such that

\(\large\ \sqrt [ 3 ]{ \sqrt [ 3 ]{ 2 } - 1 } = \sqrt [ 3 ]{ a } + \sqrt [ 3 ]{ b } + \sqrt [ 3 ]{ c }\).

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