I do not believe there is such a thing ..... Even within a single language, even native speakers interpret things differently whenever the level of speech rises above simple things.

The closest here might be music, but then the interpretation of music differs widely (independently of language), witness the sorely different appreciations of the selfsame piece of music by different individuals.

This is the right answer for sure, but if all languages have a common

core, maybe it could be possible. For example if we think of the way neurons communicate with each other.

Maybe precisely the way neurons communicate with one another illustrates why there is no possibility of such a language : whereas the elementary event of one neuron firing is broadly the same everywhere, the way the firing is processed, and the cascade of subsequent events that flows from it, totally depends on each individual brain. 

Within any brain there exist resonance pathways, etc. (which is the very reason why 'practice' in anything is required, in order to establish such resonance patterns within the brain.) After much practice, you can become a virtuoso pianist, or flawless speaker of a second language, etc. (because you established and specialized neural resonance pathways.) So that a similar event of neuron firing can give rise to extremely different processing in different brains. 

A simple example would be faintly overhearing a spoken word in, say, Mandarin - the brain of someone who has studied Mandarin would process the overheard sound very differently from the brain of someone who has never studied it.