How do we express in French that an action lasts 11 months from the moment it begins?
I'm not sure if it's supposed to be written like this "Pour les suivants onze mois" or "Pour les onze mois suivants" or something completely different.
"Les onze prochains mois" or "les onze mois suivants" would be the most usual translation for "the following 11 months" to me.
I would translate the "for" with "pendant", "durant" or "pour" depending on context.
Another usual translation (that is pretty much literally translated from the English version you provided) :
Ou un exemple au passé :
In general one would simply say "pour onze mois" or "pendant onze mois" - if the "following" idea is implicit from the context. You should provide more context to be sure.