Talking does not need to use speech to happen. Written languages are also fantastic for communication. Hint: we are communicating over one right now. But the written word is a very high-level form of communication. You should be able to recognise that Mandarin (Chinese) is a viable method of communication between two people, but that doesn't necessarily mean you can use it (yet).
What I suggest is that you find a common language between yourself and the Apes. As others have already hinted at; mathematics is a pretty fine common language. It's also fairly high-level, which makes it difficult to communicate things like "Hey, I feel hungry. Could you do me a favour and let me out of this cage so I can fetch something to eat?"
So let's rewind a bit, and choose something else.
Initially, you want something a little more practical. People and animals leak lots of information in the form of body-language. Gesturing is a more forced form body-language, and is pretty intuitive.
What this leads onto is sign language (ironically, sign language is present in the reboot Planet Of The Apes). There's no universal sign language. Most countries follow one/few standards, just like most countries have one/few accepted written languages. My knowledge of signing is very limited, but I've been told that the sign for eating is common among several of them.
Learning to sign would allow you to talk to Apes. As signing is primarily for the deaf and mute, it has the advantage of you not needing to know how to speak their language in the first place. More accurately, many of the methods employed while teaching sign don't make the assumption that the learner can already speak Ape.
Final note: If their technological level is equivalent to the 1970's then it would be safe to assume they have computers (albeit, clunky slow ones). Programming languages share lots of commonalities with maths, but allow you to phrase statements that are much more useful to communicating between two intelligent animals. Computer code also follows very strict structure. This is a boon, because structure means predictability. Patterns will emerge in the code, while you may not understand any of the letters, given enough exposure, you will correlate collections of symbols with meanings.
A 1970's computer programming Ape might be the easiest thing to talk to... so long as you have a computer.