"I too"/"I as well" can be correct in some situations in English, though less colloquial.
According to tips for the lesson Мені теж means to me (like in Could you give it to me), as far as i can remember для мене теж would mean "for me too" (Is this gift for me? Yes, this one is for me, and this one is for mee too) я теж would stand for I too (I was there too, or like in "Me too, me too! :)"). Could anybody check whether or not i am correct?
Given the lesson subject its seems that the context is like this: "I am forty" — "me too".
Thank you for the information. I don't remember the context very much now, but it would be (using english letters but ukrainian pronounciation) something like "Meni sorok rokiv. Meni tez, Victor, and as far as i know more precisely Viktore with the letter "e" for this specific name at the end of the name. Then the Vladimir_Phrolov's question somewhere here would be valid.