Let P be a polynomial, with real coefficients, in three variables and F be a function of two variables such that

$P(ux,uy, uz)=u^{2}F(y-x,z-x,z-x)$ for all real $x$, $y$, $z$, $u$,

and such that $P(1,0,0)=4$, $P(0,1,0)=5$, and $P(0,0,1)=6$. Also let A, B, C be complex numbers with $P(A,B,C)=0$ and $|B- A|=10$. Find $|C-A|$. The original answer is in the format $(m/k)\sqrt{n}$, please give the value of m + n + k.

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