SUMO-3

There exists two triples of real numbers $(a,b,c)$ such that $(a-\frac{1}{b}), (b-\frac{1}{c}), \text {and } (c-\frac{1}{a})$ are the roots to the cubic equation $x^3-5x^2-15x+3$ listed in increasing order.

Denote the two triples of real numbers by $(a_1,b_1,c_1)$ and $(a_2,b_2,c_2)$ .

If $(a_1,b_1,\text { and }, c_1)$ are the roots to monic cubic polynomial $f$ , and $(a_2,b_2, \text {and }, c_2)$ are the roots to monic cubic polynomial $g.$

What is $f(0)^3+g(0)^3=?$

SUMO: Stanford University Math Organization