Let $x, y$ and $z$ be real numbers such that $$\begin{array}{rl} x^2 +2(y-1)(z-1) &=12 \\ y^2 +2(z-1)(x-1) &=6 \\ z^2 +2(x-1)(y-1) &=9 \end{array}$$ Find all the possible values of $x+y+z$.