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Algebra Level 4

Given the sixth term of the binomial equation below equals to 84:

\[{ \left( { 2 }^{ \log _{ 2 }{ \sqrt { { 9 }^{ x-1 }+7 } } }+\frac { 1 }{ { 2 }^{ \frac { 1 }{ 5 } \log _{ 2 }{ { (3 }^{ (x-1) }+1) } } } \right) }^{ 7 }\]

Find the sum of every possible value of x

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