TO-infinitive or gerund: MEAN, HELP

Mean and help can be followed by either a gerund or a to-infinitive but with different meanings:

In those days, being a student meant spending long hours in the library. (In those days if you were a student, it meant that you spent long hours in the library.)
I didn't mean to hurt your feelings. (I didn't intend to hurt your feelings.)

I can't help thinking that you are hiding something. (only in the negative: I have to think that you are hiding something.)
Could you help me (to) undo my shoelaces? My fingers are frozen. (Could you undo my shoelaces?)

Help can be followed by a bare infinitive or a to-infinitive.