Confusing $$x, y, z$$

Algebra Level 5

$x^2y+y^2z+z^2x=xy^2+yz^2+zx^2=kxyz$

Find the range of $$k$$ for which there is at least one triplet $$(x,y,z)$$ of non-zero real numbers such that the equation above holds true.

If it is in the form $$(-\infty, a]\cup [b,\infty)$$, find $$a+b$$.

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