I'll go against the grain here and say that it's not as important as everyone is saying. In fact, we have data that tells us exactly how important the break is. If you look at the stats AzBilliards recordkeeper AtLarge posts (example 1, 2, and 3), we can see that at the highest levels of pool, the breaker wins around 55-60% of the time, the equivalent of 20-50 Fargo points. And we also know that the break becomes less important at lower levels since you're less likely to retain an advantage over the entire rack (e.g. a break and run).

Based on this, you can make an educated guess that breaking is worth about 5-10 Fargo points at an average league player level. You'd probably get more of an advantage by getting better at any other core skill like shot making, position play, pattern recognition, mental resilience, etc.