This is a famous sentence from Horace's Epistle, if I can believe Wikipedia. It's first person speech in a letter.
I'm trying to understand the grammar and produce a translation that is a bit more literal than the one provided by Wikipedia ("Not bound to swear by the words of a master").
There is actually no non in the sentence, and I wonder whether nullius means "no-one" or "nothing" here. The construction is also interesting because it's essentially a "double bind", one passive and one active: Addictus means "bound", and iurare means "swear [allegiance to]".
My own attempt would be: The writer "is bound to swear by no [nullius] teacher's words", the genitive nullius being linked to the genitive magistri, and iurare the object of addictus (which in many other uses takes a genitive). One could even try to emulate the Latin emphasis by putting the negation first: "There is no teacher whose words we are bound to swear allegiance to", or the like.
On second thought the sentence may even be more assertive: It is not the addictus that is negated, but the iurare! Perhaps a better translation would be "we are committed to take no teacher's words for granted".
Is my interpretation correct?