Let \(p(x) = x^2-5x +a\) and \(q(x) = x^2-3x+ b\) where \(a\) and \(b\) are positive integers. Suppose \( \gcd(p(x), q(x)) = x- 1\) and denote \(k(x) = \text{lcm}(p(x),q(x)) \). Find the sum of all distinct roots of \((x-1) + k(x) \).

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