The figure above shows the kinetic and potential energies of a $3 \text{ kg}$ projectile. At times $t=1 \text{ s}$ and $t = t_2,$ the kinetic and potential energies of the projectile are equal, and the projectile's respective horizontal positions at those moments are $x_1=6\text{ m}$ and $x_2 \text{ m}.$ If the horizontal position $x_2$ can be expressed as $x_2= \left(a \pm \frac{6}{5}\sqrt{b}\right) \text{ m },$ where $a$ and $b$ are positive integers, what is the value of $a+b?$

The air resistance is negligible and the gravitational acceleration is $g= 10 \text{ m/s}^2.$