This paper introduces a novel framework for proactive cross-domain resource orchestration in 6G RAN-Edge networks, featuring large language model (LLM)-augmented agents. The system comprises specialized RAN (energy efficiency) and Edge (latency assurance) agents that engage in iterative negotiation, supported by advanced reasoning and planning capabilities. Agents dynamically interact with a digital twin (DT) to test their proposals and leverage a long-term collective memory where their joint successful and failed agreements along with the related network contexts are distilled into strategies to either follow or avoid and subsequently stored. Given that agents are subject to a plethora of cognitive distortions when retrieving those past experiences -- such as primacy, recency, confirmation and availability biases -- we propose in this work a novel unbiased memory design (A reusable mockup version of the unbiased memory source code is available for non-commercial use at https://github.com/HatimChergui/unbiased-collective-memory). featuring (i) semantic retrieval of past strategies via Jaccard similarity; (ii) learning from failures through amplified weighting of SLA violations and mandatory inclusion of failed negotiation cases to mitigate confirmation bias; (iii) diversity enforcement to minimize availability bias and (iv) recency and primacy weighting with slow decay to counteract temporal biases. Evaluation results showcase the impact of existing biases and how the unbiased memory allows to tackle them by learning from both successful and failed strategies, either present or old, resulting in $\times 4.5$ and $\times 3.5$ reductions of unresolved negotiations compared to non-memory and vanilla memory baselines, respectively, while totally mitigating SLA violations as well as improving latency and energy saving distributions.