addition of necessary sources:
#stable
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echo "deb http://ftp.fr.debian.org/debian/ buster-backports main" >> /etc/apt/sources.list
echo "deb-src http://ftp.fr.debian.org/debian/ buster-backports main" >> /etc/apt/sources.list
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echo "deb http://ftp.fr.debian.org/debian/ buster-backports main contrib non-free" >> /etc/apt/sources.list
echo "deb-src http://ftp.fr.debian.org/debian/ buster-backports main contrib non-free" >> /etc/apt/sources.list
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apt update
To know how kernel are installed:
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uname -a
Good news LMDE4 already has backports repository activated by default, we use later the backports sources to update our kernel.
To search a newest kernel:
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apt search linux-image
In the output we will see a lot of kernels, but we have interest to the latest, at this time the kernel 5.7:

Lets do it and install the latest kernel:
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apt install linux-image-5.7.0-0.bpo.2-amd64 linux-headers-5.7.0-0.bpo.2-amd64 -t buster-backports -y
A reboot is needed to boot on the new kernel:
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reboot
We can check now:
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uname -a
The output:
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Linux my-pc 5.7.0-0.bpo.2-amd64 #1 SMP Debian 5.7.10-1~bpo10+1 (2020-07-30) x86_64 GNU/Linux
let's take it a step further by removing the old kernels, in general it is advisable to keep 2 kernels in case there is a problem with one of them.
To view the installed kernel:
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dpkg --list 'linux-image*'
Example to purge a kernel:
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apt autoremove --purge linux-image-5.6.0-0.bpo.2-amd64 linux-headers-5.6.0-0.bpo.2-amd64 -y
We need to upgrade the grub with the changes we made:
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update-grub2
After an reboot in the boot menu, select advanced options, you can also check the kernels who are usable.