A function $f ( x )$ that is continuous on the entire set of real numbers satisfies the following conditions.\\
(가) For $x \leq b$, $f ( x ) = a ( x - b ) ^ { 2 } + c$. (Here, $a$, $b$, and $c$ are constants.)\\
(나) For all real numbers $x$, $f ( x ) = \int _ { 0 } ^ { x } \sqrt { 4 - 2 f ( t ) } \, dt$.\\
When $\int _ { 0 } ^ { 6 } f ( x ) \, dx = \frac { q } { p }$, find the value of $p + q$. (Here, $p$ and $q$ are coprime natural numbers.) [4 points]