Makes sense, since Hungarian and Finnish belong to the same language group :)
well, they belong to the same language family, but they are different branches. it's a bit like we would say, that... spanish and german are similar, because they are both indo-european languages. :) (although there are less subdivisions/levels in Uralic language family... and the branches/groups are a bit misty :D )
I hope this can help:
Link on Wikipedia (I prefer to copy the text below the link because the article is long):
The infinitive of a verb is the form suffixed by -ni, e.g. várni, kérni. There is a variant -ani/eni, which is used with the following groups:
verbs ending in two consonants (e.g. játszani, tartani, küldeni, választani, festeni, mondani, hallani, ajánlani),
verbs ending in a long vowel + t (e.g. fűteni, véteni, tanítani, bocsátani) and the words véd and edz (védeni and edzeni respectively).
Exceptions are állni "to stand", szállni "to fly", varrni "to sew", forrni "to boil", which have -ni despite the two consonants. This is due to the fact that in written language, the "long" 'l' (or 'r') sound has to be marked.
Strictly speaking "go" is "menni" so making this imperative and first person plural (since "let's go" is "let us go") then : "menjünk".
On the other hand the english "let's go" nowadays can have a meaning like a general nudge to get doing something. I would rather say "gyerünk" in that case.