Which inequality?

Algebra Level 3

\[ \large \left(11 + \frac1{a^4} \right)^{\dfrac13} + \left(11 + \frac1{b^4} \right)^{\dfrac13} \]

If \(a\) and \(b\) are positive numbers such that their sum is 1, find the minimum value of the expression above.

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