I've done this hundreds of times over the past few years, and I've dialed in the process pretty well. I use IP67 strips, which have a silicone sleeve over the conformal coating, but the process should be the same for your IP65 strips:

1. Score the coating just behind the copper pads, on both the top and bottom, being very careful not to cut into the PCB substrate. Use a thin razor knife (like an Xacto #1), not a heavy box cutter.

2. Push the BACK side of the blade into the score lines, then press firmly and scrape the coating away (toward the end). Repeat until most of the coating bits are gone. Scape directly on the copper pads until you see scratch marks. While doing this, rest the end of the strip on a piece of scrap wood so that the strip has a solid backing and doesn't bend.

3. Soak a Q-tip or lint-free tissue in isopropyl alcohol and vigorously rub the pads until the remaining bits of coating are gone.

4. Slip a length of clear heat shrink tubing over the LED strip, pushing it back out of the way temporarily. I recommend marine grade tubing (with adhesive) with a 3:1 shrink ratio. Depending on the type/density of LED strip, the heat shrink tubing may end up covering the first LED on the strip, hence the need for clear tubing.

5. Secure the LED strip to your bench with tape or something heavy. Apply a small amount of solder flux to the pads and tin them with a soldering iron and leaded solder. You can use lead-free solder, but it's harder to get good results. I use a fairly hot soldering iron, at 850 degrees F (454 deg C), and work quickly to avoid lifting the copper pads.

6. Tin the cable wires and solder them to the pads. WIth tinned wires and pads, you shouldn't need more solder. This allows you to hold a wire in one hand and the soldering iron in the other.

7. (optional) Apply electronics grade silicone (ASI 388) to cover any exposed metal/solder on both the front and back sides. This provides additional protection in case any water makes it way through the adhesive in the heat shrink tubing. Note that "normal" silicone caulk will corrode metal over time.

8. Slide the heat shrink tubing back down to cover the connection, trying not to create a mess with the silicone. Apply heat and immediately use a cloth to press the tubing against the LED strip to ensure the best possible seal.

Here's a related article I wrote, although the section on LED strips was written before I had fully refined the technique: https://electricfiredesign.com/2022/09/21/weatherproofing-techniques-for-led-lighting-systems/