10. Let $\mathrm{f}$ be a real-valued function with the rule $\mathrm{f}(x)=x^{3}+3 x^{2}+6 x+14$ defined for all real value of $x$. It is given that $a$ and $b$ are two real numbers such that $\mathrm{f}(a)=1$ and $\mathrm{f}(b)=19$. Find the value of $(a+b)^{2}$.