A Very Special Number

Computer Science Level 4

Find the smallest positive integer \(n\) such that the first 10 digits of \(\sqrt[3]{n}\) contain all the digits from 0 to 9 exactly once each.

Clarification: For example, the first 4 digits of \(\sqrt[3]{2} = 1.25992\ldots\) are 1, 2, 5, and 9.