Let \( {a}_{1},{a}_{2},{a}_{3}\cdots \cdots \cdots {a}_{11}\) be real numbers satisfying
\( {a}_{1}=15,27-2{a}_{2}\gt 0\;and {a}_{k}=2{a}_{k-1}-{a}_{k-2}\) for \( k=3,4\cdots \cdots \cdots\;11.\)
If \( \frac{{a}_{1}^{2}+{a}_{2}^{2}+\cdots \cdots +{a}_{11}^{2}}{11}=90,\) then the value of \( \frac{{a}_{1}+{a}_{2}+\cdots \cdots +{a}_{11}}{11}\) is equals to _______.