\[ \Large {\int} \large \frac{dx}{\sqrt[2013]{(x-1)^{2012} (x+1)^{2014}}} \]

Given that the integral above is defined for \(x > 1\). Ignoring the arbitrary constant, it evaluates to \(\large{ \frac{ \alpha}{\beta} \left( \frac{x - \lambda}{x + \mu} \right)^{\sigma / \theta }} \) where \(\alpha, \beta, \lambda, \mu, \sigma, \theta \) are positive integers with \( \gcd(\alpha, \beta) = \gcd(\sigma, \theta ) = 1 \). Find the value of \(\alpha+ \beta+ \lambda+ \mu+ \sigma+ \theta + 6033\).

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