I saw this sentence in an episode of attack on titan the speaker is referencing a power she has and that she doesn't understand how it works unlike the listeners who do
The english sub translation was
Unlike you Im basically clueless (about the power)
My understanding of the sentence goes like this
その辺の仕組みは - "The mechanics\structure\details of this thing (the power)"
あんたらと違って - "You guys (the listeners) are different"
I believe 知らん is short for 知らない so my best translation of the last line would be
よう知らん - In the way in the way in which you dont know
If this translation were correct wouldn't it make more sense to say よう知てる what am I missing here