Value Plugging May Not Help ...

Algebra Level 5

The sum of all values of \(x\) that satisfy

\[\large{\sqrt [ 3 ]{ 6(5x+6) }-\sqrt [ 3 ]{ 5(6x-11) }=1},\]

can be expressed as \(\dfrac{m}{n},\) where \(m\) and \(n\) are coprime integers. Find \(m+n.\)

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