Let the lines $$L_1 : \vec{r} = \lambda\hat{i} + 2\hat{j} + 3\hat{k}, \lambda \in R$$ and $$L_2 : \vec{r} = \hat{i} + 3\hat{j} + \hat{k} + \mu(\hat{i} + \hat{j} + 5\hat{k}); \mu \in R$$, intersect at the point $$S$$. If a plane $$ax + by - z + d = 0$$ passes through $$S$$ and is parallel to the lines $$L_1$$ and $$L_2$$, then the value of $$a + b + d$$ is equal to ______.