Suppose two polynomials of degree 3, \(f(x), g(x)\) have three distinct positive integer roots each, and there is no common root between both polynomials. (In other words, the set of roots of these polynomials has 6 distinct elements.)

Also, \(f(x)-g(x)=r\) for some real number \(r\) for all real values of \(x\).

If \(S(P(x))\) denotes the sum of absolute values of coefficients of a polynomial \(P(x)\), find the minimum possible value of \(S(f(x))+S(g(x))\).

This problem is part of the set ... and polynomials

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