How far away can you be to hear a dungeon?

This "sound" does not indicate a dungeon. This is what is referred to as "ambience".

Ambient sounds can be played in any dimension, including the Nether and the End, and can be heard in both singleplayer and multiplayer. Ambience can occur in a space of any size, but they seem much more likely to be heard in larger spaces that are completely filled with a light level lower than 8, without any lighting from the sky. Ambience is more likely to play from the direction of darker spaces. The space does not need to be sealed off or hidden - ambience can be heard from a space that the player can actually see - nor does the player need to be underground to hear ambient sounds.

There are many different types of ambient sounds, each one applying to a different part of the world - above ground, underground, the Nether and the End; but none indicate anything particularly special about the surrounding area.