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 ____________.