very few economists agree that raising the minimum wage by X dollars will result in prices rising by X dollars so that the effect is non-existent

You are looking for obvious increase in prices, but raising prices is unpopular with consumers.

Instead, companies will move the production offshore, lay people off, make smaller packages [2], use machines, use cheaper ingredients etc. and those things create the illusion that the price is not rising. Price is the same, but the quality (of goods/services & of life in communities) is going down.

  cost of labor isn't the only input in pricing

It's the main one, since the biggest cost to most companies are employees + suppliers (that also have their own employees). Increase in the price of labor will certainly have an effect - if not directly on higher prices, then on quality.

  [2] https://en.wikipedia.org/wiki/Shrinkflation

Of course it will affect price, I never said that it wouldn't. The argument is that it doesn't have an effect large enough to negate the extra income.