Base 11 is called undecimal[1] and Wikipedia has a comprehensive list[2]. It doesn't list 59 but it would be enneaquinquagesimal if you follow the rules.

[1] https://en.wikipedia.org/wiki/Undecimal

[2] https://en.wikipedia.org/wiki/List_of_numeral_systems#Standa...

- Use Latin for 1-10

- Use Latin 10n, 10n+1 and 10n+2

- Use Greek for the units + Latin for the tens for 10n+3..10n+9

The Greek-Latin mixup was probably caused by whoever invented the word hexadecimal (16). The older "sexadecimal" was maybe avoided due to the word "sex". "sedecimal" would be a bit more correct Latin but it doesn't seem to be attested.

it was simply very common to use Greek prefixes in Latin to indicate measures.

Micro, mega, nano, etto, etc. are all Greek words.

  micro -> mikrós (small)
  mega -> mégas (big)
  nano -> νάνος (small in its own kind)
  etto -> ἑκατόν (100)

there were absolutely no issues with the word sex, sexagesimal (from the Latin sexagesimus which meant the 60th) is still a thing.

They seem very similar to ordinals and partitive numerals in Spanish. Those words are being quickly forgotten except low values and powers of ten. But they were common knowledge years ago, I guess it was the same for other romance languages.

Sexagésimo/a is 60th or 1/60. So sexagesimal is very natural.