Find the equations of the horizontal and vertical asymptotes for the function f(x)=(6x³+54)/(x³-9x). Which of the following options correctly describes the asymptotes?

A) Horizontal asymptote: y = 6; Vertical asymptotes: x = -3, x = 3
B) Horizontal asymptote: y = 0; Vertical asymptote: x = 0
C) Horizontal asymptote: y = 1; Vertical asymptotes: x = -3, x = 3
D) Horizontal asymptote: y = -6; Vertical asymptotes: x = -3, x = 3