\[ \sin (A) \sin(2A) \sin(3A) \sin(4A) = ax^2 + bx^3 + cx^4 + dx^5 \]

If \( \sin^{2}(A)= x \) and that the equation above is satisfied for constants \(a,b,c,d\), then find the value of \( 12a - 10b +8c -11d \).

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