\[ \large \displaystyle\int_0^1 \ln\left(\sqrt{1-x} + \sqrt{1+x}\ \right)\ \mathrm{d}x= \dfrac{1}{A}\ln(B) - \dfrac{1}{C} + \dfrac{\pi}{D} \]

If \(A,B,C,D\) are positive integers, where \(B\) is not a perfect power, evaluate \( A+B+C+D\).

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