Answer
$\sqrt{\frac{k_1+k_2}{m}}$
Work Step by Step
We use Newton's second law to find:
$m \frac{d^2x}{dt^2}=F \\ m \frac{d^2x}{dt^2}= -k_1x-k_2x \\ m \frac{d^2x}{dt^2}= -x(k_1+k_2) $
We see from this equation that k is equal to the sum of $k_1$ and $k_2$, so it follows:
$ \omega = \sqrt{\frac{k}{m}} = \sqrt{\frac{k_1+k_2}{m}}
$
