Next week????

Hello every body.
My questions are about the pronouncation of t in these cases:
(next week,next day,left side).
and m instead of n in (one more)
My questions are :
Is it important to delete t in my voice and say m instead of n?
Is there any rule in english explaining that?

Thank you so much.........

"next week": these are fine, ne[ks] week/day, ne[kst] week/day
"left side": these are fine, le[f] side, le[ft] side.

Here's the reason speakers don't always pronounce [t]. The letters , for example, in the word next are pronounced [kst], that's three sounds. Three sounds take more time and energy to pronounce than two sounds, so speakers drop the last sound, [t].

"one more": these are fine, o[m]e more, o[n]e more

The sound change above has to do with anticipation. Both [n] and [m] share the same manner of articulation; they are nasals. The speaker in anticipation of the in more pronounces as [m], giving o[m]e more.

Hope that helps. :-D