Complex Numbers and Quadratic Equations: JEE Main 2021 Mathematics question

Let z be those complex numbers which satisfy | z + 5 | $\le$ 4 and z(1 + i) + $\overline z$(1 $-$ i) $\ge$ $-$10, i = $\sqrt { - 1}$. If the maximum value of | z + 1 |² is $\alpha$ + $\beta$$\sqrt 2$, then the value of ($\alpha$ + $\beta$) is ____________.