Thas right, how do I get it out?
A high tech option if all else fails:
Freeze the whole thing in liquid nitrogen (-196 celsius or colder)
Steel has a linear expansion coefficient of about 11x10^-6 per degree C. Brass about 18-19. So for example the brass might shrink by about 0.15% compared with the die
Not seriously suggesting this.
The good news is that you pulled the head away from the rest of the case in the die, rather than it separating inside the rifle when shooting it, which just might have been an even bigger problem, or danger. And much more of a worry to extract the remnants.
At the worst, if none of these ideas do it, you are down by the cost of a die.
I'm guessing that that case was already suffering from incipient case head separation. As may be some others from that batch. Maybe you've been taking your reloads too many times, and missing the signs.
AFAIK most stuck cases are due to inadequate lube, or trying to resize a badly overblown cases from a rifle with a loose chamber. Mostly just tearing off the rim rather than detaching the head from the rest of the case.
These ones are simple enough to sort, drill, tap and pull out the case (might mess up the depriming pin if you can't pull back the rod far enough), or uniquely with a Lee die, slacken off the rod, even take off the securing collet, and pound it out.
That said, I've never stuck a case yet, touch wood, though thought I nearly have a couple of times. Which I attributed to listening some (nonsense ??) idea that you should hold the case in the die for several seconds before withdrawing it. Some idea that it took a little while for the case to to settle down, BS in retrospect. But I think allowed the lube to creep away so withdrawing the case became noticeably more difficult.
So my technique is to move the ram up all the way, then down again, in one smooth motion.