Let $0 \le x,$ $y,$ $z \le 1.$  Find the maximum value of
\[f(x,y,z) = x^2 y + y^2 z + z^2 x - xy^2 - yz^2 - zx^2.\]The answer is in the form rac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.

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