Probably like most non-Americans, I find the Americans near-homonyms sometimes confusing.

The theme song for the H.R. Pufnstuf TV show went "He can do a little but he can['t] do enough", which mystified me before I was a linguist. In the environment N-D of "can('t) do" it's impossible for the T to be distinctly pronounced, so it has to be left to pitch and length.

A little-known phonetic fact about English (and I don't know whether this is just English or whether it's more general) is that vowel length can be correlated with pitch. In "bead" the long vowel drops, in "bid" the short vowel has a slight rise in pitch: though these effects can be masked by grammatical or semantic uses of pitch.

Better known is the lengthening effect of voice: "bead" is longer than "beat", and "bend" is longer than "bent". The effect is slighter in "ben" vs "bent".

Some such combination of factors is operating in American "can" vs "can't" but I have to leave it to native speakers to determine exactly what.