(Remember, don't mash up "Java and C++" with "static typing". Java and C++ are not worth mentioning when discussing type systems; they have type systems that get in the way and make it harder to code.)
Do you know of any good resource to read up about a better type system and its benefits, but without having to learn a whole new language? (I don't have time to learn a new language, but this sounds important enough to read up on).
What I mean is, when I write a function to do something with files, I don't want to have to decide whether I'm going to accept a "FILE" class or not. This isn't laziness: it's realizing that I will one day want to use a different class which looks like a file, but isn't part of the "file" hierarchy.
This situation comes up far more often than one might think, and it saves a lot of headaches up-front (designing complicated hierarchies to prevent future use-cases you'll want).
From what I've read, Type inference doesn't help with that. (But I haven't read much, so I could be wrong).
Experience may help you change your mind. Reading papers and advocacy from people who've used it should provide limited influence.
As an aside, there are solutions to programming problems I would've never come up with if it weren't for experience in other programming languages, so I read "don't have time to learn a new programming language" as "don't have time because I haven't learned a new programming language."
That's one way, or you could write clear unambiguous code such that the types are reasonably self evident.