How can I free up space on my iPhone 11 Pro Max?

Did you check the recommendations your iPhone can give you in Settings/General/iPhone Storage -> Recommendations?

You will also see a list of apps using most of your storage space.

In most cases, you can save space by reducing your photos.

But, if you use iCloud Photos, deleting the photos from your iPhone will also deleted them in iCloud.

You will have to transfer the photos from iCloud to your computer first, as described here:

Archive or make copies of the information you store in iCloud - Apple Support

Try deleting old messages, emails, and photos. After deleting them, go to the Trash and delete them again.

Try these steps as well:

Manage your iCloud storage - Apple Support