Nested Cube Roots

Algebra Level 2

If \( \sqrt[3]{ \frac{80}{27} +\sqrt[3]{ \frac{80}{27}+\sqrt[3]{ \frac{80}{27} +... }}}\) =\(\frac{a}{b} \) where a and b are co-prime numbers.

What is the value of \(a+b\)?

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