Let the set of all values of \( k \in \mathbb{R} \) such that the equation \( {z}(\overline{z}+2+i)+k(2+3i)=0, \; z \in \mathbb{C} \), has at least one solution, be the interval \( [\alpha,\beta] \). Then \( 9(\alpha+\beta) \) is equal to:
\( -10 \)
\( -8 \)
\( 10\sqrt{13} \)
\( 8\sqrt{13} \)
