There exist two triples of real numbers \((a,b,c)\) such that \(a-\frac{1}{b}, b-\frac{1}{c}, c-\frac{1}{a}\) are the roots to the cubic equation \(x^3-5x^2-15x+3\) listed in increasing order. Denote those \((a_1, b_1, c_1)\) and \((a_2, b_2, c_2)\). If \(a_1, b_1,\) and \(c_1\) are the roots to the monic cubic polynomial \(f\) and \(a_2, b_2,\) and \(c_2\) are the roots to the monic cubic polynomial \(g\), find \(f(0)^3+g(0)^3\).

Let's think step by step and output the final answer within \boxed{}.
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