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I have two objects in my scene cube and plane, and I have set up 2 different worlds. is it possible to assign a world node which will influence the specific object in my scene, One world for the Cube and another world for the plane so they can be influenced by the settings I tweak.
I don't think you can have 2 world backgrounds that can be accessed separately by objects, however, you can "fake" it by mixing a Glossy Shader with your main Texture, and having an Environment Texture connected to the Glossy Shader (make sure to use environment texture and not image texture). Use the Reflection Texture Coordinate as an input vector for your image. Use a different Environment texture (mixed with the main texture) for each object you want different. In the image below, I have a different "background" for each of the cubes, and both are different than the HDRI world environment:
