Birational geometry of blow-ups of projective spaces along points and lines

Consider the blow-up X of P^3 at 6 points in very general position and the 15 lines through the 6 points. We construct an infinite-order pseudo-automorphism on X. The effective cone of X has infinitely many extremal rays and, hence, X is not a Mori Dream Space. The threefold has a unique anticanonical section, which is a Jacobian K3 Kummer surface S of Picard number 17. The restriction of \phi_X on S realizes one of Keum's 192 infinite-order automorphisms. We show the blow-up of P^n (n>=3) at (n+3) very general points and certain 9 lines through them is not a Mori Dream Space. As an application, for n at least 7, the blow-up of \bar{M}_{0,n} at a very general point has infinitely many extremal effective divisors.