It's a long equation

Algebra Level 4

If \(S\) is the sum of all real \(x\) satisfying

\[\left( 6x-3 \right) \sqrt { 7-3x } +\left( 15-6x \right) \sqrt { 3x-2 } =2\sqrt { -9{ x }^{ 2 }+27x-14 } +11,\]

what is the value of \(S\)?

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