Suppose \triangle A B C is such that A B=13, A C=15, and B C=14. It is given that there exists a unique point D on side \overline{B C} such that the Euler lines of \triangle A B D and \triangle A C D are parallel. Determine the value of \frac{B D}{C D}. (The Euler line of a triangle A B C is the line connecting the centroid, circumcenter, and orthocenter of A B C.)