Value Plugging May Not Help ...

Algebra Level 5

The sum of all values of xx that satisfy

6(5x+6)35(6x11)3=1,\large{\sqrt [ 3 ]{ 6(5x+6) }-\sqrt [ 3 ]{ 5(6x-11) }=1},

can be expressed as mn,\dfrac{m}{n}, where mm and nn are coprime integers. Find m+n.m+n.

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