This is going to be some flavour of Classical Japanese style conjugation, so if you like you can just go for “I understand the basic meaning in context so I’ll skip past it without too much thought” the same way you might for a bit of dialogue in Tohoku dialect.
I think this is the Classical auxiliary む, which follows the mizenkei of a verb (same stem that you use for ~ない negatives). This む has a sound change to ん when it’s at the end of a sentence or before a noun (technically, when it’s in shushikei or rentaikei form). It has an annoyingly large set of possible meanings, but my reference says that when it’s at the end of a sentence in the first person it’s expressing intention: “I intend to VERB, I will VERB”.
(This auxiliary eventually ended up as the volitional form in modern Japanese – 食べよう、飲もう – which keeps at least some of the various senses classical む had, including the statement of intent one – see the “expressing your will” section of the Tofugu article on the volitional.)