Make a list of all possible rational zeros of $f(x)=3x^3-11x^2-35x+75,$ and then use this list to find all of the functions's rational zeros, if any exist.

If the answer is not an integer, enter it as a fraction. If there are multiple zeros, separate the answers with commas $(0).$ If no rational zeros exist, enter "none".

Rational Zero Candidates: $+-|1,\frac{1}{3},3,5,\frac{5}{3},15,25,\frac{25}{3},75$:$|$

Rational Zeros: