$\mathfrak{Square}^{\mathfrak{Square}}$

The squares 1, 25, 49 are pairwise relatively prime and in arithmetic progression. Let $x_1^2, y_1^2, z_1^2$ and $x_2^2, y_2^2, z_2^2$ be the next two smallest triples with this property when value is measured by the $z_n$ 's. Find $z_1+z_2$ .

Note: This problem is not original.