Who's up to the challenge? 66

$\large\sum _{ n=0 }^{ \infty }{ \dfrac { { L }_{ 2n+1 } }{ (2n+1)^{ 2 } \binom{2n}{n}} }$

Let $L_n$ denote the $n$ th Lucas number , where $L_1 = 1$ , $L_2 = 3$ and $L_n = L_{n-1} + L_{n-2}$ for $n \ge 3$ .

If the series above can be expressed as $-\dfrac\pi A \ln\left( B - C\sqrt D+ E\sqrt{F - G\sqrt H} \right) + \dfrac IJ K ,$

where $A$ , $B$ , $C$ , $D$ , $E$ , $F$ , $H$ , $I$ and $J$ are positive integers , with $I$ and $J$ being coprime integers; $D$ , $E$ and $H$ square-free; and $K$ denotes the Catalan's constant , find $A+B+C+D+E+F+G+H+I+J$ .