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Calculus Level 5

\[\int _{ 0 }^{ 1 }{ \frac { \log { \left( x \right) { \left( \log { \left( 1-x \right) } \right) }^{ 3 } } }{ x } dx } =A\zeta \left( 2B+1 \right) -\frac { { \pi }^{ c } }{ D } \zeta \left( 2E+1 \right) \]

\(A,B,C,D,E\) are positive integers. Find \(A+B+C+D+E\).

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