Alaric is right. There is a giant pile of unsafe junk out there in "LED bulbs", and the ones you tried fit that description. There's more detail on this issue
here. If you can return them for your money back, do so. If you can't, then throw them out and chalk it down as a lesson.
The only two 1157 LED bulbs that will
possibly work OK are
these and
these. Electrically either of them will work fine once you install an LED-compatible turn signal flasher, that is
this kind. It has a ground wire the original flasher does not have, so you'll need to find a nearby convenient good ground to attach the new wire to. Shouldn't be difficult to find a good ground under the dash close to the flasher. The new flasher will work with LEDs, regular bulbs, or any combination. The LED bulbs to try in the back-up lights are
these, and the ones to try in the front turn signals are
these. Side marker lights would be
these front and
these rear.
This "try" and "possibly" type of language is because you cannot just pop in an LED, say "Yep, it lights up bright and dim, so we're good", and drive off. LEDs are a basically different kind of light source than the type the lamp was designed to use, so you have to carefully check the light distribution to make sure it's safe and adequate. How to do so is described
here.
Also, be aware that if you put LEDs in the front turn signals and/or the front side marker lights, you will have to do some rewiring. The side markers are hooked up with one wire to the parking lamp feed and one wire to the turn signal feed, so that they provide two functions: a steady-burning side marker light whenever the parking/headlights are on, and a blinking turn signal repeater when the turn signal is operating. This only works if both the front turn signal bulb and the front side marker bulb are filament type; it does not work with LEDs and makes problems with feedback causing improper operation of lights all over the car. You would need to move the one side marker wire that's presently connected to the turn signal feed, so that it runs from the side marker light to ground. That will let you use LEDs without problems, but it will also delete the turn signal function of the side marker lights. If you want to keep the turn signal operation of the side markers (a very good idea especially in a large car like a '76 Fleetwood!), you would need to install the control module described at
this page.
There is no lamp-outage detection circuit on a '76 Cadillac, so you don't need warning cancellers or load resistors. Your car may be equipped with a lamp-indicator system based on fiberoptic cords transmitting some light from the lamp itself to an indicator box inside the car (or on the front fenders facing rearward so you can see them from the driver's seat). These are not affected by the type of bulb installed.