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I can come close.

There is a Spatter filter in Photoshop that can be found in Filter>Brushstroke>Spatter. However, I confess that I don't fully understand how this filter works and I have not been able to find any good explanation of it. If you simply paint a single color swatch on a blank layer and apply the filter, it does nothing. But if any two or more colors are touching on that layer, then the filter works by creating a spatter effect wherever those different colors are touching.

Anyway, here's a rather convoluted way of getting your effect.

• Start with a bottom layer with your background color:

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• On a new layer above that, use the Text tool to enter your text.
• It would be best if you found a distorted font that already looks like your end product, but I started with a "normal" font (Cooper Std) and then (later) distorted it myself.
• Make a selection of this text. On a new blank layer, fill that selection with black. This layer will later be used for the drop shadow, but for now, turn off its visibility.

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• Go back to your text layer and add a layer mask. Using a hard black brush in the mask, distort the text... something like this:

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• Now copy the entire image—distorted text plus background—onto a new layer using Stamp Visible (Shft+Ctrl+Alt+E).
• Convert this layer to a Smart Object.
• Go to Filter>Brush Strokes>Spatter. Experiment with the settings. I used Spray Radius=4 and Smoothness=3.
• The Smart Object enables you to go back later and re-adjust these settings, if you wish. You can also optionally add a small gaussian blur to soften the hard edges.

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• Using the magic wand, select the white text and copy it to a new blank layer.
• Turn off the visibility of all other layers except for the bottom background layer.
• Now turn on the visibility of the black shadow layer you created earlier. Manually position it into place.
• Here's what I've got:

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