It's complicated because we are talking about several distinct but potentially overlapping statuses. The main consequence of the EU long-term resident status is that if you gained it in one participating EU country, it's somewhat easier to move to another participating EU country. In particular, you can move first and apply for a residence permit from within the destination country (as opposed to having to wait for a visa or permit outside the country). However, you still need to apply for a resident permit. You may also be asked to prove you have stable and sufficient resources and health insurance to get the new residence permit and being a long-term resident in one EU country doesn't automatically grant you the right to work in another EU country.
Importantly, you would not immediately become an EU long-term resident in your new country of residence. The logic of the directive is that you should qualify for a renewable residence permit as long as you fulfill the conditions and until you become an EU long-term resident again (after five years). If you were to lose your status in the new residence country before that, your earlier residence country has an obligation to readmit you. In other words: what you have now is a guarantee that if something should go wrong in Germany in the next 5-6 years, you have a strong right to come back to the Czech Republic.
Furthermore, the EU long-term resident status is not necessarily equivalent to a national settled or permanent resident status nor does it automatically qualify you to apply for citizenship. In many cases, people might qualify for all of these around the same time but they are still legally distinct and it's possible to qualify for one but not the other. Citizenship in particular is entirely under the control of each member state, your status under EU law has no bearing on that.
If that wasn't complicated enough, note that by moving with your Czech partner to Germany, you probably qualify for a completely different status: family member of an EU citizen. It's attractive because the formalities are relatively simple, income requirements are lower or non-existent and if you qualify for that status, you have a very strong right to remain in the country with your partner. You would also have an unconditional right to work in Germany, which is not the case with the EU long-term resident route.
Eventually, after five years under the EU citizen family member status, you would become a Permanent resident in Germany. This is the strongest of all the possibilities I listed. Once you have that, it's virtually impossible to force you to leave the country, even if you have no means to support yourself anymore or, depending on the nature of your partnership, if you separate from your partner.
Finally, for the sake of completeness, note that there are exceptions to all this for public policy, public security or public health reasons. If you are found guilty of a serious crime, are suspected of terrorism, etc. all bets are off, none of these statuses will prevent Germany from expelling you. That's why I used the phrase very strong right. Unlike citizenship, EU law doesn't give you an absolute right to stay in a country.
