An algebra problem by Sakanksha Deo

Algebra Level 5

\[\frac{1}{ \sqrt[7]{531441} + \sqrt[7]{472392} + \sqrt[7]{419904} + \sqrt[7]{373248} + \sqrt[7]{331776} + \sqrt[7]{294912} + \sqrt[7]{262144} } \]

The expression above simplifies to \( \dfrac{ \sqrt[7]{a} - \sqrt[7]{b} + \sqrt[7]{c} }{d} \), where \(a,b,d\) are coprime positive integers with \(a>b\).

Find \( a - b + c + d \).

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