Given the equation $x^{3}-13 x^{2}+24 x-22=0$ has a complex root $1+i$, then the real root of this equation is
7. 11.

By the Conjugate Root Theorem, the equation has a root $1-i$. By Vieta's formulas, the real root of this equation is $\frac{22}{(1+i)(1-i)}$ $=11$.