A great tool is the 20Mb SuperGrubDisk2 bootable iso. It works like an emergency grub/osprober and sniffs out all bootable OS on your system, no matter if the Os' bootloader is working or broken. Put it on a stick, boot from it and pick your Mint install.
If you get to a desktop either run
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sudo update-grub
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sudo grub-install dev/sda
Actually, if you got plenty of usb slots burn SuperGrubDisk2 on one of those tiny drives that don't stick out and just leave it there; if ever a grub update messes up you're covered.
Of course you can try SuperGrubDisk2 even when all's working fine, just see if you can boot from it; it should offer you options to boot either XP or Mint or , by picking the 'boot grub.cfg', hand the boot over to your working grub.