I will try to simplify them.
Using the live Mint, you need to mount your / partition, sda6
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sudo mount /dev/sda6 /mnt
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for i in /dev /dev/pts /proc /sys /run; do sudo mount -B $i /mnt$i; done
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sudo chroot /mnt
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update-initramfs -u
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grub-install --recheck /dev/sda
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update-grub
Press CTRL-D again to exit the terminal