Mori Dream Spaces are generalizations of toric varieties and, as the name suggests, Mori’s minimal model program can be run for every divisor. It is known that for n>=5, the blow-up of P^n at r very general points is a Mori Dream Space iff r<=n+3. In this talk we proceed to blow up points as well as lines, by considering the blow-up X of P^3 at 6 points in very general position and all the 15 lines through the 6 points. We find that the unique anticanonical section of X is a Jacobian K3 Kummer surface S of Picard number 17. We expect that there exists an infinite-order pseudo-automorphism of X, whose restriction to S is one of the 192 infinite-order automorphisms constructed by Keum. A consequence is that there are infinitely many extremal effective divisors on X ; in particular, X is not a Mori Dream Space. As an application, this implies that the blow-up of P^n+3 at (n+3) very general points and the 15 lines through 6 of them is not Mori Dream. This is an ongoing joint work with Lei Yang.